Exploration of similarities between classical wave mechanics and quantum mechanics

This dissertation explores classical analogs of one particle wave mechanics and multiparticle quantum entanglement by using classical wave optics. We develop classical measurement techniques to simulate one particle wave mechanics and quantum entanglement for up to four particles. Classical simulation of multi-particle entanglement is useful for quantum information processing (QIP) because much of the QIP does not require collapse and decoherence is readily avoided for classical fields. The simulation also allows us to explore the similarities and differences between quantum optics and classical wave optics.; We demonstrate the simulation of one particle wave mechanics by measuring the transverse position-momentum (Wigner) phase-space distribution function for a classical field. We measure the Wigner function of a classical analog of a Schrödinger cat state. This Wigner phase-space distribution function exhibits oscillatory behavior in phase space and negativity arising from interference of two spatially separated wave-packets in the cat state. The measurement of Wigner functions for classical fields has practical applications in developing new coherence tomography methods for biomedical imaging.; We develop a classical method to simulate projection measurement in coincidence detection of two entangled photons. This is accomplished by using an analog multiplier and a band pass filter. We measure the classical analog of the joint probability of detection of two photons for the entangled states{09}$12$[|H₁V₂⟩ ± |V₁H₂⟩] and $12$[|H₁H₂⟩ ± |V₁V₂⟩], where H is horizontal polarization and V is vertical polarization. Our measurement method reproduces nonlocal Einstein-Podolsky-Rosen (EPR) correlations for four polarization-entangled Bell states of two particles and violates Bell's inequality. A most interesting result of our measurements is the experimental simulation of three and four particle Greenberger-Horne-Zeilinger (GHZ) entanglement for the entangled states $12$[|H₁H₂ H₃⟩ + |V₁V ₂V₃⟩] and $12$[|H₁H₂ H₃H₄⟩ + |V ₁V₂V₃ V₄⟩] respectively. We are able to reproduce the 32 elements of the GHZ polarization correlations between three spatially separated superposition beams which leads to a conflict with local realism for nonstatistical predictions of quantum mechanics. That is in contrast to the two entangled particles test of Bell's inequalities, where the conflict arises for statistical predictions of quantum mechanics. (Abstract shortened by UMI.)...